I'm just learning about doing some LED and/or El wire effects for my project, and really need some 101 info. What i want to accomplish is to have a roughly 10 foot long by 2 foot high panel of lights which are simulating an ocean wave, primarily in shades of blue. Where do I start, and what have you learned?

You're going to be using individually addressable LEDs that use shift registers to "talk" to each light.. such as the WS2801 strips that The Tunnel of Questionable Enlightenment used a couple of years back. There are also individual kits such as the Cool Neon kit, but your best bet will be the strips depending on your application. You would use a small arduino type clone board to run them such as the Teensy 3.0 or many others.

It would be in this way that you could tell each LED exactly what color to be and when to illuminate.. making a wave pattern or anything else that you need.

The programming for these is NOT easy and has a very steep learning curve if you've never worked with them. Do some google searching for WS2801 and you'll find a wealth of info out there such as forums on Sparkfun, Adafruit, etc. There are also a few people around that might be able to assist if you due your own due diligence and dive in head first..

What are you putting them on? Is it a flat, rigid panel? Will there be flex involved? Why kind of material?

Oh boy, when somebody starts asking what my budget is and another says "steep learning curve" I start to think I may be using the wrong approach. I'm building an MV and I need to light it up for night. It's a raft, so I was thinking of doing a series of lights that would look like water. MV is about 12 feet long, and sits about 3 feet off the playa. Budget is small, a few hundred dollars, for the lighting.

Individually-controlled-LED strips sell, wholesale, for about $10/meter. Your car is about 3-4 meters in length, so that means about $30 per row of lights. To make a "panel" you need multiple rows, and usually you'll want the LEDs to be equally spaced vertically as they are horizontally. Here is where the LED density comes in. Some strips have about 60 LEDs/meter (~18/ft), some have less, at 30 LEDs/meter (~9/ft) or 32/m. If you want a 2-foot high panel, you need a number of rows equal to the number of LEDs that fit into 2ft.

So for example, you want a 2ft x 12ft (say it's 3m) sheet of 60LED/m strips:

$10/m x 3m x 2ft x (18 / ft) = $1,080

For 30 LED/m, it is half that price.

You don't need to have equal axis density if you're combining the LEDs with other effects. For example, you could have a back-lit blue panel, and then use the LEDs for "shimmer" and small waves like in the background of Sonic the Hedgehog's Green Hill Zone:

Overall, you should plan out what kind of effect you really want to get out of this with the budget you've got and then work around that.

"The essence of tyranny is not iron law. It is capricious law." -- Christopher Hitchens

I'd recommend using the WS2811 strip with the IC built into the LED. Fewer pins, therefore more robust. I use the gel coat variety for a bit of added strength and weatherproofing.

Unless you fancy yourself as a coder or you know someone who is good with Arduino (or similar) – and is up to the job of doing the math to produce a water pattern, I recommend you go for an ‘off the shelf’ controller. On a budget, your best bet is to get an SD Programmable controller from one of the online Chinese suppliers. You should be able to get one pretty cheap. Look for one that comes with software that will allow you to import video files. With a bit of experimentation you should be able to create/plagiarize a video or animation of the effect you want and convert it into a data file for the controller to play back on your LED panel.

Be wary of adding too many LEDs to each controller port. The WS2811 isn't that fast, so the controller may not be able to update all the LEDs quick enough if you push it too hard.

Also, you'll need a lot of power. To use BBadger's example, 108m of 60 LED/m strip could peak as high as 160 Amps at 12V. Normal running of a pattern would probably be around 60A at 12V. Thus, you need to inject power at regular intervals. Of course, if you were using 5V strip, you’d need some very heavy duty wiring indeed …Obviously, don’t use my figures – check the precise spec of the strip you order, and then test a short length with a multi-meter as the specs are sometimes wrong

If you’re using 5V strip, you'll be needing a bunch of very chunky regulators...

Given your budget, you'’ll probably have to stick to about 30 LED/metre. Obviously it won’t give you as much detail, but (for example) the coat in my avatar pic is 32/m and as you can see, the effect is still good. This would allow you to use a cheaper controller, have easier to manage power requirements and be half the price. If ordering from China, always get more than you need - a spare or two may well come in handy!